# Uncertain dates with Tempo

```elixir
Mix.install([
  {:ex_tempo, "~> 1.6"},
  {:tz, "~> 0.28"}
])

Calendar.put_time_zone_database(Tz.TimeZoneDatabase)
import Tempo.Sigils
```

## Real data is not precise

Historians, archivists, genealogists, and anyone parsing messy records meet dates like *"sometime in the 1560s"*, *"the 15th of some month in 1985"*, *"1984 or 1986"*, *"around 2000, give or take a year"*. Most libraries force these into a false precision. Tempo represents each one faithfully — as ISO 8601-2 / EDTF values with real semantics — and answers questions about them without pretending to know more than the data does.

## Masks — unknown digits

An `X` is an unknown digit. `~o"156X"` is *some year in the 1560s* — one value spanning the whole decade, iterable and comparable like any other:

```elixir
Tempo.explain(~o"156X") |> IO.puts()
```

A mask *above* concrete finer units is subtler: `~o"1985-XX-15"` is *the 15th of some unknown month of 1985*. One actual day occurred — we just don't know which of twelve candidates. Materialising expands the candidate set:

```elixir
{:ok, candidates} = Tempo.to_interval(~o"1985-XX-15")
Tempo.IntervalSet.count(candidates)
```

## One-of sets — enumerated possibilities

When the record says *"1984 or 1986"*, that's not a span — it's an epistemic choice between listed values:

```elixir
Tempo.explain(~o"[1984,1986]") |> IO.puts()
```

## Margins — plus or minus

*"Around 2000, give or take a year"* is a value with an uncertainty margin. The margin is not decoration — it widens every question you ask. A value of `2000±1Y` could ground anywhere in 1999–2001, so overlapping 1999 is possible, and overlapping 1997 is not:

```elixir
around_2000 = ~o"2000±1Y"

{
  Tempo.overlap_certainty(around_2000, ~o"1999"),
  Tempo.overlap_certainty(around_2000, ~o"1997")
}
```

## Qualifications — uncertain and approximate

EDTF's `?` (uncertain) and `~` (approximate) attach to values and travel through operations:

```elixir
{~o"1984?", ~o"2004~"}
```

## Asking questions that respect the uncertainty

Here is the point of all this representation: the **certainty API** gives three-valued answers — `:certain`, `:possible`, or `:impossible` — computed over every grounding the uncertain value admits.

Was *some year in the 20XXs* within the 21st century? Every grounding is:

```elixir
Tempo.within_certainty(~o"20XX", ~o"2000Y/2100Y")
```

Shrink the window by one year and a single grounding (2000) escapes — so the answer honestly degrades:

```elixir
Tempo.within_certainty(~o"20XX", ~o"2001Y/2101Y")
```

Do two `±`-qualified events overlap? Depends how far apart they are:

```elixir
{
  Tempo.overlap_certainty(~o"2000±1Y", ~o"2001±1Y"),
  Tempo.overlap_certainty(~o"2000±1Y", ~o"2010±1Y")
}
```

The crisp predicates come in `certainly_*` and `possibly_*` pairs — the modal square of the same underlying relation set:

```elixir
{
  Tempo.certainly_before?(~o"2000±1Y", ~o"2010"),
  Tempo.certainly_before?(~o"2000±1Y", ~o"2001"),
  Tempo.possibly_before?(~o"2000±1Y", ~o"2001")
}
```

## A worked example — dating an artifact

A ledger entry is dated *the 15th of some month in 1985*. A fire destroyed the archive on June 20, 1985. Could the entry have been written before the fire? Must it have been?

```elixir
entry = ~o"1985-XX-15"
fire = ~o"1985-06-20"

{
  Tempo.relation_certainty(entry, fire, :precedes),
  Tempo.possibly_before?(entry, fire),
  Tempo.certainly_before?(entry, fire)
}
```

> *"The entry **possibly** precedes the fire — the January-through-June 15ths do, the July-through-December ones don't — but not **certainly**. If the fire had been in 1986, every candidate would precede it:"*

```elixir
Tempo.certainly_before?(entry, ~o"1986-01-01")
```

## Where next

* The [uncertain dates guide](https://hexdocs.pm/ex_tempo/uncertain-dates.html) covers the full EDTF surface and how qualifications propagate.
* The [temporal formalisms guide](https://hexdocs.pm/ex_tempo/temporal-formalisms.html) explains the theory: Allen's algebra, the certainty lattice, and why intervals are the only entities.
* The [getting started livebook](getting-started.livemd) if you arrived here first.